This invention relates to plotting apparatus in general and more particularly to an improved plotting apparatus wherein in operation, a modifying system introduces a significant time delay between the generation of a dependent variable quantity and the plotting thereof against an independent variable quantity.
The two quantities will hereinafter be referred to as the dependent variable and the independent variable, respectively.
The range of applications and usefulness of the present invention is best illustrated with specific reference to a spectrophotometer, both as regards the background discussion and the description of practical embodiments which follow.
In a spectrophotometric context, the dependent variable is identifiable with percentage sample transmission or absorption and the independent variable with wavenumber or wavelength scan. Reference to transmission and wavenumber will henceforth be assumed to include absorption and wavelength as possible respective alternatives.
Sample percentage transmission is generated in the form of a varying flux of suitable radiation handled by a modifying system that transduces the flux into correspondingly varying electrical signals, filters the signals to reduce their noise bandwith, routes them to the pen servo of a strip chart recorder and finally plots them as the ordinate against an absicssa slaved to the wavenumber scan.
The modifying system inevitably includes components with a finite, although substantially constant, electrical response. This, and the deliberate holding of electrical signals for the performance of specific functions within the system, such as digital computation, cause a time delay between the occurrence of a radiation flux change and the plotting of the corresponding electrical signal change that can be regarded as essentially fixed for any given instrument design and independent of any operational parameter selected.
The filter for limiting the noise bandwith is not, of course, one of the aforesaid components. Its response is strictly related to its time constant, which is one of the parameters that fundamentally affects the operation of a spectrophotometer and which, therefore, must be chosen with certain performance criteria in mind. This effectively means that the filter is bound to superimpose upon the fixed delay referred to a further delay which varies with the choice of its time constant. In other words: the total time delay introduced by the modifying system is variable.
While the modified sample transmission signal is being held up, the wavenumber scan is naturally proceeding at whatever rate the user has selected. By the time the electrical signal is recorded, the abscissa has moved ahead by a number of abscissa units, i.e., wavenumbers, which depends on the total signal delay encountered in the modifying system and the wavenumber scan rate is use. As a result, sample percentage transmission is plotted with a positional phase lag with respect to the wavenumber scan (assuming, of course, that corresponding instantaneous values of the two variable quantities are considered) and consequently fidelity of the plot must suffer.
More specifically, if the variable time delay and the fixed time dealy introudced by the modifying system are denoted as f and t, respectively, f+t is clearly the total time delay between the generation of sample percentage transmission as an optical signal and the corresponding electrical signal being recorded on the chart. Now, if S is the scan rate in wavenumbers per second, S(f+t) must naturally represent the wavenumbers scanned in time T, or in other words, the positional phase lead of the abscissa, which must, of course, be numerically equal to the positional phase lag of the plotted ordinate referred to the abscissa.
To appreciate the generality of the expression S(f+t), it will be sufficient to generalize the meaning of S as units of the independent variable passed per second.
It is assumed that the total time delay is substantially constant irrespective of the rate of change of the electrical signal or is made so by introducing suitable known means in the modifying system.
In the description that follows, the phrase "dependent phase lag" refers to the positional phase lag in plotting the dependent variable and the phrase "independent phase lead" refers to the positional phase lead in plotting the independent variable, both in terms of units of the independent variable. Furthermore, the phrase "phase tracking means" refers to the tracking of either the dependent phase lag or the independent phase lead, bearing in mind the equivalency therebetween as regards establishing the amount of dependent phase lag caused by the total time delay due to the modifying system.
It should be understood, moreover, that the term "plotting" refers to any suitable representation of the manner in which the dependent variable changes with respect to the independent variable and is in no way limited to the recording of a trace upon a chart. Computer printout or oscilloscope displays are examples of alternatives to be included within the meaning of the term.